Void growth and coalescence in porous plastic solids

Koplik, Joel; Needleman, A.

doi:10.1016/0020-7683(88)90051-0

Cited by 737 publications

(474 citation statements)

References 27 publications

(71 reference statements)

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“…For the two larger values of the stress ratio, ρ, it is seen that introducing voids in the material leads to overall softening of the material during void growth. This is due to void growth toward coalescence (Koplik and Needleman, 1988). For ρ = 0.75 the strain level at which the softening begins is significantly smaller than for ρ = 0.50 (T ≈ 1.3), due to much more dramatic void growth at low strains.…”

Section: Resultsmentioning

confidence: 88%

“…The largest value of ρ = 0.75 corresponds to the triaxiality ratio T ≈ 3.3, which is roughly the triaxiality in in the vicinity of a crack tip for lightly hardening solids (Koplik and Needleman, 1988). Figure 3b the size of the cell (R v /R c = 0.2) the void volume fraction is f ≈ 5.33 · 10 −3 .…”

Section: Resultsmentioning

confidence: 88%

“…Defining the triaxiality ratio, T , as the ratio of the macroscopic effective stress to the macroscopic hydrostatic stress gives the following relation (Koplik and Needleman, 1988)…”

Section: Numerical Methods and Problem Descriptionmentioning

confidence: 99%

“…Extensive 1 research has been directed toward modeling void growth and coalescence in order to obtain a quantitative understanding of the influence of void distribution, material properties and loading, on the basic mechanisms of void growth, and on bulk properties such as material response and fracture toughness (see e.g. Rice and Tracey, 1969;Needleman, 1972;Gurson, 1977;Tvergaard, 1982;Koplik and Needleman, 1988;Kysar et al, 2005;McElwain et al, 2006).…”

Section: Introductionmentioning

confidence: 99%

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Void growth to coalescence in a non-local material

Niordson

2008

European Journal of Mechanics - A/Solids

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-The size-effect in metals containing distributed spherical voids is analyzed numerically using a finite strain generalization of a length scale dependent plasticity theory. Results are obtained for stress-triaxialities relevant in front of a crack tip in an elastic-plastic metal. The influence of different material length parameters in a multi-parameter theory is studied, and it is shown that the important length parameter is the same as under purely hydrostatic loading. It is quantified how micron scale voids grow less rapidly than larger voids, and the implications of this in the overall strength of the material is emphasized. The size effect on the onset of coalescence is studied, and results for the void volume fraction and the strain at the onset of coalescence are presented. It is concluded that for cracked specimens not only the void volume fraction, but also the typical void size is of importance to the fracture strength of ductile materials.

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Section: Resultsmentioning

confidence: 88%

Section: Resultsmentioning

confidence: 88%

“…Defining the triaxiality ratio, T , as the ratio of the macroscopic effective stress to the macroscopic hydrostatic stress gives the following relation (Koplik and Needleman, 1988)…”

Section: Numerical Methods and Problem Descriptionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Void growth to coalescence in a non-local material

Niordson

2008

European Journal of Mechanics - A/Solids

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“…the critical void volume fraction f c and the value at failure f f , from the literature are applied. Note that for a single f 0 the values of f c and f f as fitted to cell model simulations [8][9][10] differ among each other and deviate considerably from the heuristically chosen parameter set in [3]. The obtained R-curves are shown in fig.…”

Section: Resultsmentioning

confidence: 97%

Simulation of Crack Propagation under Small‐Scale Yielding by means of a Non‐local GTN‐Model

Hütter

Linse

Mühlich

et al. 2011

Proc Appl Math and Mech

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Today, the local approach to fracture is widely applied to simulate the failure of specimens. For ductile damage processes the Gurson-Tvergaard-Needleman model is the quasi-standard. In the last time non-local extensions allowed a mesh-size independent simulation of crack growth. However, most publications dealing with this subject focus upon the convergence regarding global quantities such as the load-displacement relation. Minor attention is paid to the fields directly at the crack tip. Correspondingly, the interrelationship between the intrinsic length of the model and relevant microscopic damage processes at the crack tip is only partly established until now. In the present study the crack propagation is simulated for an implicitly gradient enriched GTN-model within a boundary layer in order to overcome influences of the specimen geometry. The different stages of damage evolution are resolved by a fine mesh. ModelIn order to describe the ductile crack initiation and propagation a non-local extension of the widely used GURSON [1] model with the modifications of TVERGAARD and NEEDLEMAN (GTN,[2,3]) is employed. For this purpose, the volumetric plastic strain rate ε vol in the evolution equation of the local model for the void volume fraction f is replaced by its non-local counterpart ε nl using an implicit gradient enrichment [4]:Thereby, an intrinsic length scale l nl is introduced via the prefactor of the LAPLACE-operator ∆Ô Õ. The formulation can be interpreted as a spatial average over the local volumetric plastic strain ε vol around the actual point. The crack propagation behavior of the model is investigated under small-scale yielding conditions by means of a boundary layer approach. This has the advantage that a possible influence of the specimen geometry can be excluded. The hardening is described by a power law (exponent N ). In the FE-model elements with quadratic shape functions for the displacements and linear ones for the non-local strains are used, for details see [4]. Dynamic simulations are performed with implicit time integration under quasi-static loading [5].In the initial loading stages the plastic deformations occur within a region much smaller than the intrinsic length scale l nl . Hence, at this stage no void growth but pure crack tip blunting is predicted by the model which is physically reasonable. In order to handle the strain singularity at the crack tip coinciding with blunting of an ideal sharp crack, an initial radius is used at the crack tip, see fig. 1. This procedure allows to use elements with edge lengths h lig considerably smaller than the value of h lig Ô0.5 . . . 2.5Õ l nl used in the literature [6,7] where numerical problems with distorted elements were reported for finer meshes [7]. For comparison, simulations without rounded crack tip were performed as well. Fig. 1 Details of the finite element mesh at the crack tip with initial radius l nl ResultsFirst, simulations with a common set of parameters (f 0 0.01, f c 0.15, f f 0.25, N 0.1, E 250 σ y , ν 0.3) and several spat...

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An iterative method for coupling of deformation and failure mechanisms on different length scales

Gänser

Fischer

Werner

2000

Int. J. Numer. Meth. Engng.

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An iterative method for coupling of numerical simulations on two length scales is presented. The computations on the microscale and on the macroscale are linked via a suitable macroscopic constitutive law. The parameters of this material law depend on the deformation history and are obtained from simulations using microstructurally representative volume elements (RVEs) subjected to strain paths derived from the associated material points in the macroscopic structure. Thus, di erent constitutive parameter sets are assigned to di erent regions of the macrostructure. The microscopic and macroscopic simulations are performed iteratively and interact mutually via the strain paths and the constitutive parameters, respectively. As an example, the strip tension test for a porous material is modelled using the ÿnite element (FE) method. The coupling procedure, the material law and its numerical implementation are described. The method is shown to allow for a detailed simulation of the deformation mechanisms both on the micro-and the macroscale as well as for an assessment of their interactions while keeping the computational e orts reasonably low.

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Void growth and coalescence in porous plastic solids

Cited by 737 publications

References 27 publications

Void growth to coalescence in a non-local material

Void growth to coalescence in a non-local material

Simulation of Crack Propagation under Small‐Scale Yielding by means of a Non‐local GTN‐Model

An iterative method for coupling of deformation and failure mechanisms on different length scales

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